The British Broadcasting Corporation, which takes very seriously the task of teaching the English how to speak, has just published this guide to pronunciation, diction and grammar. Written by no less an authority than Robert Burchfield, chief editor of the Oxford English Dictionaries, it is often surprisingly lenient. Citing a sentence of Graham Greene's as a precedent, Burchfield declines to forbid absolutely the use of ''like'' as a conjunction. The BBC reports, for example, that the error of confusing ''disinterested'' with ''uninterested'' ''attracts more unfavorable comment from listeners than any other word, with the possible exception of 'hopefully.' '' But Burchfield does not pander to the public. The use of ''alternative'' to mean one of several possibilities, instead of simply one of two, is ''vigorously resisted by listeners but impossible to avoid in many contexts,'' he says. On the other hand, he is vigorous and definite in his condemnation of such clichés as ''scenario,'' ''at this point in time'' and ''no way,'' Americanisms, he says, that have crept into English speech. But throughout it all, he takes a soothingly long historical view of the evolution of language, noting that it has survived other disruptions considerably more serious than whatever may be happening to it now. As examples, he cites the loss of grammatical gender in Early Middle English and the great vowel shift at the beginning of the 15th century, when nearly every vowel changed (''hoose'' became ''house,'' and ''gose'' became ''goose''). Reassuringly, he concludes, ''Any argument based on the assumption that the changes occurring in the English language in Great Britain at present are more serious or more objectionable than those that have occurred in the last 1,200 years is almost certainly false.''